Why Google?

Well, Google apps come pre-installed on Android phones, the phone can be associated (and locked) with a Google account and its possible to conveniently backup and restore using your Google account, so why not Google?

How do I backup and restore the contacts on an Android phone using a Google account?

* Note: The steps below apply for both backup and restore since it involves syncing.

Part 1: Enable backup to Google servers

1. Navigate to Settings > Backup & reset

2. Tick both Back up my data and Automatic restore

Part 2: Associate the phone with a Google account

1. Navigate to Settings > Account and select Add account

2. Select Google from the list

3. If you have an existing account, select Existing, else, create a Google account first be clicking New

4. Wait while Google gathers some information about the phone

5. Enter the Google account email and password then tap the Next icon (triangle pointing right)